\newproblem{lay:5_1_23}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 5.1.23}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Explain why a $2\times 2$ matrix can have at most two distinct eigenvalues. Explain why a $n\times n$ matrix can have at most $n$ distinct eigenvalues. 
}{
  % Solution
	The eigenvalue problem
	\begin{center}
		$|A-\lambda I|=0$
	\end{center}
	implies finding the roots of a polynomial of degree $n$ ($|A-\lambda I$). Since a polynomial of degree $n$ can have at most $n$ distinct roots, then $A$ can have 
	at most $n$ distinct eigenvalues.
}
\useproblem{lay:5_1_23}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
